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Author Topic: Split-Complex Numbers?  (Read 2420 times)
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Forums Freshman
Posts: 19

« on: March 10, 2010, 02:53:05 PM »

I was wondering if anyone here knew anything about the Split-Complex numbers, and if you can make interesting fractals with them.

Thanks in advance,
Fractal Senior
Posts: 1863

« Reply #1 on: March 10, 2010, 04:14:59 PM »

http://kram1032.deviantart.com/art/dusty-old-attic-128907426 - this is a Buddhabrot with Split Complex numbers wink

Nice but not really interesting.

However, playing with it a bit more can lead to quite interesting results smiley

Dual Numbers result in this Fan-pattern:

And if you cycle through complex, split complex and dual numbers, you get quite interesting patterns like this one:
Fractal Fertilizer
Posts: 362

The pwnge.

« Reply #2 on: March 11, 2010, 01:02:58 AM »

Neat pics. I'm surprised that the Fan pattern (dual numbers( also produces an interesting image, as the x is independent of the y, and so would always approach either a steady state or infinity... and so y will "almost always" goes to infinity too, if x goes to infinity. If x goes to a steady state, then y will either go to infinity as well (albeit only exponentially fast), or go to a steady state. No, wait... x could be chaotic... never mind.  embarrass

My computer is broken, could someone render a quick escape-time picture of dual numbers? It would be appreciated!  smiley

Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
Fractal Senior
Posts: 1863

« Reply #3 on: March 11, 2010, 06:40:57 PM »

I also found it kinda surprising smiley
The split complex (at least for the standard Mset) aren't half as interesting as the dual numbers smiley
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